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Structural equation modeling with latent variables guide

skills/analysis/statistics/sem-guide/SKILL.md

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# Structural Equation Modeling Guide

Build, estimate, and evaluate structural equation models (SEM) with latent variables using Python (semopy) and R (lavaan), including confirmatory factor analysis and path analysis.

## What Is SEM?

Structural Equation Modeling is a multivariate statistical framework that combines factor analysis and path analysis to test complex theoretical models involving:

- **Observed (manifest) variables**: Directly measured (e.g., survey items, test scores)
- **Latent (unobserved) variables**: Theoretical constructs measured indirectly through observed indicators (e.g., "motivation," "intelligence")
- **Structural paths**: Directional relationships between variables (regression-like)
- **Measurement model**: How latent variables relate to their indicators (CFA)
- **Structural model**: How latent variables relate to each other (path analysis)
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